How do you solve the system of equations: 2x + y = 1 and 4x + 2y = −1?
1 Answer
Explanation:
Start by writing the system as given to you
#{(2x + y = 1), (4x + 2y = -1) :}#
Notice that you can simplify the second equation by dividing all the terms by
#4/2 * x + 2/2 * y = -1/2#
This is equivalent to
#2x + y = -1/2#
Notice that the left side of the second equation is identical to the left side of the first equation, but that this expression equals two different values,
In other words, you have
#{(2x + y = 1), (2x + y = -1/2) :}#
Let's say that you wanted to solve this system by substitution
#y = 1 -2 x#
#2x + (1 - 2x) = -1/2#
#color(blue)(cancel(color(black)(2x))) + 1 - color(blue)(cancel(color(black)(2x))) = -1/2#
#1 color(red)(!=) -1/2#
Since